Hypercube queuing model for emergency facility location problem considering travel and on-scene service times

Document Type : Research Paper


1 Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


The hypercube queuing model is a descriptive model for emergency systems in which servers are mobile and serve customers at their locations. In emergency systems, the service time of each server includes the travel time from the server station to the customer's location, the on-scene time and the travel time from the customer's location to the server station. The on-scene service time depends on factors such as server expertise and the severity of the customer’s situation while the travel times depend on factors such as vehicle type, the path, and the traffic volume. Therefore, it is necessary to consider and analyze these two times separately. In the hypercube queuing model presented in this study, the service time is divided into two sections, the travel time and the on-scene service time, both of which follow independent exponential distributions with known rates. A new system state is defined in which the status of servers is classified into idle, serving at the customer's location and traveling. By solving the equilibrium equations with the Gaussian- Elimination method (for small size examples) and simulation (for larger examples), limiting probabilities are obtained, and performance measures (such as the ratio of the on-scene time to the total server busy time) are evaluated. A case study of the road emergency stations of the Red Crescent, which are based in Hamadan province, Iran, is also used to check the model's real-world performance.


Main Subjects

Ansari, S., McLay, L. A., & Mayorga, M. E. (2017). A maximum expected covering problem for district design. Transportation Science51(1), 376-390.
Ansari, S., Yoon, S., and Albert, L. A. (2017). An approximate hypercube model for public service systems with co-located servers and multiple response. Transportation Research Part E: Logistics and Transportation Review, 103, 143-157.
Boyaci, B., and Geroliminis, N. (2012). Facility location problem for emergency and on-demand transportation systems. 91th annual meeting of the transportation research board, Washington D.C.
Boyaci, B., and Geroliminis, N. (2014). Hypercube queueing models for emergency response systems. 14th Swiss Transport Research Conference.
Boyaci, B., and Geroliminis, N. (2015). Approximation methods for large-scale spatial queueing systems. Transportation Research Part B, 74, 151-181.
Budge, S., Ingolfsson, A., and Erkut, E. (2009). Approximating vehicle dispatch probabilities for emergency service systems with location-specific service times and multiple units per location. Operations Research, 75(1), 251-255.
Budge, S., Ingolfsson, A., and Zerom, D. (2010). Empirical analysis of ambulance travel times: the case of calgary emergency medical services. Management Science, 56(4), 716-723.
Davoudpour, H., Mortaz, E., andHosseinijou, S. A. (2014). A new probabilistic coverage model for ambulances deployment with hypercube queuing approach. International Journal of Advanced Manufacturing Technology, 70, 1157-1168.
Geroliminis, N., Kepaptsoglou, K., and Karlaftis, M. G. (2011). A hybrid hypercube – genetic algorithm approach for deploying many emergency response mobile units in an urban network. European Journal of Operational Research, 210, 287-300.
Ghobadi, M., Arkat, J., and Tavakkoli-Moghaddam, R. (2019). Hypercube queuing models in emergency service systems: A state-of-the-art review. Scientia Iranica, 26(2), 909-931.
Halpern, J. (1977). The accuracy of estimates for the performance criteria in certain emergency service queuing systems. Transportation Science, 11(3).
Iannoni, A. P., Chiyoshi, F. Y., and Morabito, R. (2015). A spatially distributed queuing model considering dispatching policies with server reservation. Transportation Research Part E, 75, 49-66.
Iannoni, A. P., Morabito, R., andSaydam, C. (2011). Optimizing large-scale emergency medical system operations on highways using the hypercube queuing model. Socio-Economic Planning Sciences, 45, 105-117.
Karimi, A., Gendreau, M., and Verter, V. (2018). Performance approximation of emergency service systems with priorities and partial backups. Transportation Science, 52(5), 1235-1252.
Kim, S. H., and Lee, Y. H. (2016). Iterative optimization algorithm with parameter estimation for the ambulance location problem. Health care management science, 1-21.
Larson, R. C. (1974). A hypercube queuing model for facility location and redistricting in urban emergency services. Computers and Operations Research, 1, 67-95.
Larson, R.C. and Sasanuma, K., (2010). Congestion pricing: A parking queue model. Journal of industrial and systems engineering, 4(1), 1-17.
Panahi, P. (2020). Emergency facility location problem considering permanent and temporary stations (case study: Hamadan province), Unpublished master thesis, University of Kurdistan
Rajagopalan, H. K., Saydam, C., Setzler, H., and Sharer, E. (2011). Ambulance deployment and shift scheduling: An integrated approach. Journal of Service Science and Management, 4(01), 66.
Rodrigues, L. F., Morabito, R., Chiyoshi, F. Y., Iannoni, A. P., and Saydam, C. (2017). Towards hypercube queuing models for dispatch policies with priority in queue and partial backup. Computers & Operations Research, 84, 92-105.
Rodrigues, L. F., Morabito, R., Chiyoshi, F. Y., Iannoni, A. P., & Saydam, C. (2018). Analyzing an emergency maintenance system in the agriculture stage of a Brazilian sugarcane mill using an approximate hypercube method. Computers and Electronics in Agriculture, 151, 441-452.
Sudtachat, K., Mayorga, M. E., andMcLay, L. A. (2014). Recommendations for dispatching emergency vehicles under multi-tiered response via simulation. International Transactions in Operational Research, 21(4), 581-617.
Toro-Díaz, H., Mayorga, M. E., McLay, L.A., Rajagopalan, H.A., and Saydam, C. (2014). Reducing disparities in large-scale emergency medical service systems. Journal of the Operational Research Society, 1-13
Yazdanparast, R., Hamid, M., Azadeh, A., and Keramati, A. (2018).  an intelligent algorithm for optimization of resource allocation problem by considering human error in an emergency department. Journal of industrial and systems engineering, 11 (1), 287-309.
Yoon, S., and Albert, L. A. (2017). An expected coverage model with a cutoff priority queue. Health Care Management Science, 21(4), 517-533.